Question

show that polynomial x4+4x2+6 has no zero

Answer 1

Answer: It is proved that there are no zeros in the polynomial $\bold{x^{4}+4 x^{2}+6}$  

Polynomial: It is defined as the expression which consist of variables that performs operations like addition, subtraction, multiplication and also non-negative integer exponential operation.

Polynomials can have no zero values since they are basically expressed in the form of equation.

Solution:

$\begin{array}{l}{\text { The roots of } x^{4}+4 x^{2}+6 \text { are }} \\ {x^{4}+4 x^{2}+6=x^{4}+4 x^{2}+4+2=\left(x^{2}+2\right)^{2}+2} \\ {\left(x^{2}+2\right)^{2}+2 \text { are the factors }} \\ {\left(x^{2}+2\right)^{2}+2=0} \\ {\left(x^{2}+2\right)^{2}=-2}\end{array}$

Hence it has no zeroes.